Non-Linear Programming Models

Overview and Rationale

This assignment is designed to provide you with hands-on experiences to optimize 

shipments via non-linear programming models in real-life applications. You are provided 

with a logistics scenario and you are asked to create a model to optimize cost and 

distribution of shipments. You are also asked to apply the Hodrick-Prescott Filter to a time 

series stock data.

Course Outcomes

This assignment is directly linked to the following key learning outcomes from the course 

syllabus:

CO1: Use descriptive, Heuristic and prescriptive analysis to drive business strategies 

and actions

CO4: Incorporate general industry practices in end-to-end analytics development 

cycles, including data management, data engineering, analytics modeling, optimization, 

and strategic development

Assignment Summary

This assignment consist of two parts. In Part I, you will use R to determine the optimal 

number of units to be transported from each source to each destination. In Part II, you will 

apply the Hodrick-Prescott Filter to a time series problem.

Part I: Transshipment Problem

This part of the capstone project is to be entirely completed in a separate Excel workbook. 

After completing part 1, please save your workbook as: 

ALY6050-Capstone-Part1-Last Name-First Initial.xlsx, and submit it as an attachment. 

There is no need to include a Word document for this portion of the project. 

The following network describes a transshipment scenario in which there are four sources 

A, B, C, and D, there are four destinations P, Q, and R, and S, and there are three 

intermediary distribution centers X, Y, and Z as shown. Each line segment indicates an 

existing shipping route, and the value next to each line segment represents the cost of 

shipping for one unit of an item from the source on the left of that line to the destination on 

the right of it. Furthermore, each of the three intermediary distribution facilities X, Y, and Z 

can handle only up to 50,000 units to be loaded/unloaded at that facility. The sources’ 

supplies capacities and the destinations’ demands are given in the following table.

Sources Supplies Destinations Demands

A 35,500 P 23,500

B 42,200 Q 36,000

C 19,000 R 40,700

D 25,500 S 19,800

Set up this transshipment problem R to determine the optimal number of units to be 

transported from each source to each destination. Use the LpsolverAPI in R to solve the 

problem. Highlight the optimal transportation cost in your report.

Part II: Applications of Quadratic Programming

The Hodrick-Prescott Filter (Decomposition) is a mathematical method used in real 

business cycle theory in economics to decompose a time series into its cyclical and trend 

components. Its formulation is based on the following quadratic programming problem: 

Let 𝑿𝒕 be the logarithm of a time series (hence, itself a time series). The Hodrick-Prescott 

filtering decomposes 𝑿𝒕

into its cyclic component 𝑪𝒕 and its trend component 𝑻𝒕 (that is, 

𝑿𝒕 = 𝑪𝒕 + 𝑻𝒕) such that the following quadratic objective functional is minimized:

 

As for the multiplier 𝝎, Hodrick and Prescott recommend 𝝎 = 𝟏𝟎𝟎 for an annual time 

series, 𝝎 = 𝟏𝟔𝟎𝟎 for a quarterly time series, and 𝝎 = 𝟏𝟒𝟒𝟎𝟎 for a monthly time series.

1. Perform a research about the Hodrick-Prescott decomposition and provide insights 

about its historical development. 

2. Interpret each term of the Hodrick-Prescott objective function, and discuss a few 

advantages and disadvantages of this decomposition method. 

3. Consider the quarterly time series of Honeywell (HON) stock prices (courtesy of 

https://finance.yahoo.com given in the Excel workbook: Week 6 Project-part 2-

Data.xlsx. Apply the Hodrick-Prescott optimization method to decompose the logarithm 

of the given time series into its cyclic and trend components. Use R to solve the 

problem.

4. Interpret the results obtained from step 3, above, and discuss the merits of your 

decomposition, in Word; if any.

5. Plot the line plots of the original time series along with its trend component on the 

same chart.

6. Use the results of your decomposition method and write a summary conclusion of your 

findings in Word.

Hint: Note that the Hodrick-Prescott decomposition of the logarithm of a time series is 

an additive decomposition; thus this decomposition becomes a multiplicative type of 

decomposition for the original time series. In other words, if y is the original time series 

and if 𝒙 = 𝒍𝒐𝒈(𝒚), then the decomposition 𝒙 = 𝒄 + 𝒕 for x implies that 𝒚 = 𝟏𝟎 𝒄+𝒕 =